Doodles Do Algebra – Lesson 7


Update: This Lesson Is Part of Book 1 of Doodles Do Algebra: “Starting Out With Mental Algebra” available on Amazon.


Teacher’s Notes:

Today your child begins using the concept of an unknown, or “x”, in order to simplify problems. DoodleOne, or darling daughter doodle, explains this in the cartoon and walks your child through a sample problem. For this math lesson, it really helps to walk your child through the steps, even if you are reading from the answer. What matters most is that he really understands how to do the problem, not if he can do it independently at this stage.



Available in the book, “Starting Out With Mental Algebra, Book 1 of Doodles Do Algebra”



The Doodle Daily today walks your child through the process of assigning x as an unknown and relating that unknown to the number of kids in the various classes Penny and her sisters attend at Co-Op.

If x represents the number in Grammar              x

what represents the number (of kids) in Geography?              3x (because there are 3 times as many kids studying Geography as Grammar)

in Math?              2 times 3x, or 6x (because there are twice as many kids studying Math as Geography, which can be represented by 3x)

6x – x is represented by the number of kids in Math minus the number of kids in Grammar, (this is just to check your child’s comprehension of how the x’s relate to the number of kids in each class and to make the next step easier to understand)

Now, There are 10 more kids in Math than in Grammar so (keeping in mind that there are more kids in Math) if we subtract the kids in Grammar from the kids in Math, we will be left with 10 kids. [You can show this with a pile of pennies (say for Math kids) and nickels (for Grammar kids). Make sure to point out that there are ten more pennies than nickels, and then have your child take one away from each pile (pennies and nickels) until none are left. This is a hands on way of showing the subtraction of kids in Grammar from kids in Math, in case you get that blank stare that comes shortly before tears of frustration as you explain the problem.] Getting back to the problem, this means that 6x – x is actually 10,

What is x equal to?              If 6x’s minus one x is 10, then 5 x’s (6 x’s minus one x) is 10, and x is 2.

So there are 2 kids in Grammar (that was equal to our x)

There are 6 kids in Geography (that was equal to our 3x)

And there are 12 kids in Math (that was equal to our 6x, or twice the number in Geography).


Please give me any feedback you have (good or bad) in the comments below!